Blue Bird Group, Indonesia's largest taxi operator, is banking on its initial public offering (IPO) to fuel growth.

The company plans to sell at least a 20 percent stake that could raise up to $400 million and is expected to be Indonesia's largest IPO this year. The offering was originally scheduled for 2013, but a family lawsuit against Bluebird's President Director Purnomo Prawiro over share ownership and trademarks delayed regulatory approval. A district court dismissed that lawsuit in February.

"It is [entirely] a family dispute so it should not disturb the company... but psychologically, people were affected. We managed to win the courts so I hope that will give authorities and investors confidence," Noni Purnomo, president director of Blue Bird Group, told CNBC's "Managing Asia."

Noni, the third generation leader of the family business, hopes the listing will help the firm thrive for generations to come.

"We want to be a quality-driven sustainable company, so being public can [help to] incorporate a transparent corporate governance system and change public perception," she said. "We've had corporate and family governance in place for the past 10 years, but people still see us as a pure family company. We want to change that."

Bay Ismoyo | AFP | Getty Images

A scene of the roads in Jakarta, Indonesia.

Taking off

Blue Bird was founded by Noni's grandmother in 1972. It's named after L'oiseau Bleu, a French fairy tale about a girl and a blue bird who work tirelessly to find happiness. The blue exterior of its 28,000-strong fleet is a common sight in Indonesia, where the company's reputation for being clean and reliable makes it unique.

Its use of technology and a neutral stance on politics underlie Blue Bird's success, but advice from founding matriarch Mutiara Djokosoetono is the secret ingredient: "My grandmother taught us to see every problem as a challenge. If we can overcome the challenge, that means we have grown better," the 45-year-old said.

Challenges were stacked against Blue Bird from the outset given female leadership in a male-dominated industry.

"I would drive a taxi once in a while to get honest opinions from customers and hang out with the drivers [though] some of them still cannot accept a female taxi driver," Noni said.

But being a woman has its advantages: "When we had a demonstration in Bali, we had to do negotiations. Being the only women in the room, I think, made a difference," she said. "People were really angry in the beginning but because I was smiling and shaking their hands, they cooled off."

Expansion plans

Blue Bird may be Indonesia's largest taxi company, but it still has plenty of room to grow.

Jakarta has 1.4 taxis per 1,000 residents, compared with 10 in Bangkok and 5.3 in Singapore, according to a Euromonitor report.

The firm is also focused on growing its logistics arm, which currently accounts for 10 percent of overall revenues.

"With a growing middle class and the opening of economy within ASEAN, I think a lot of foreign investors will invest in Indonesia, especially factories. With that, they'll need reliable good quality logistic services so the growth for that will be exponential," Noni said. "I see this as a huge opportunity for us because we already have a good experience in handling people and fleet."

"I am planning to grow it pretty fast [for] the first 5 years," she added. "In 10 years' time hopefully it can be almost [the] same size as Blue Bird's passenger transport."